Find the following limits if they exist. Must show all work (analytically?): 1. lim f(x) where f(x) = (-3x + 8 if x <-2 X-2 %3D 2x ifx >-2 2. lim 14+h) -f(4) where f(x) = x- 8x + 7 %3D

Q: Consider the function f(x)=(x4 -2x3)/(x-2). Verify that Lim (x->2) f(x)=8. In order to guarantee…

A: Consider the function f(x)=(x4 -2x3)/(x-2). To Verify that limx→2f(x) = 8

Q: If x- 2 1 lim -2 f(x) – f(2) then, the slope of the tangent line at the point (2, f(2)) is m =7. %3D…

A: By limit defination of f'(x) at point x= a

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

A:

Q: If 4.x 9 <f(x) < x² - 4x + 7 for x 0, find lim f(x).

A:

Q: lim(1 + 3x)²/x x→0

A: Concept if limx→0f(x) = 1    and limx→∞g(x) = ∞ then the limx→0f(x)g(x)  = elimx→0[f(x) -1][g(x)]…

Q: 6. Consider the function f Cx)=5(o+5)-25 if X#し if xfO D.IS fCx) continuous at X-0? EXPlain

A:

Q: Let f(x) = 5 and g(x) = 3x + 1. Use the definition above to verify the following limits:

A: We have to verify the result: a  limx→7 fx=5b  limx→4 gx=13 Where function is given that: fx=5,…

Q: If lim H(h) = x and. lim H(h) = y , then find lim H(h3 – h) h→04 h→0-

A:

Q: 4. x- 1 lim x- Vx + 5-3

A:

Q: If 3x − 5 ≤ f(x) ≤ x² − 3x + 4 for x ≥ 0, find_lim f(x). x →3

A: given  3x-5≤f(x)≤x2-3x+4for x≥0

Q: 3. (a) Differentiate the function f(x) = x2 from first principles.

A:

Q: If 3x – 1 0, find lim f(x). X→3

A: Given query is to find the indicated limit.

Q: Given f(x) = 7x - 6; x < 6 x ≥ 6, 4x + 3 ; Find: lim x →6 f(x)

A:

Q: f(x) = √x, a = 1

A: Givenf(x)=x a=1To findlimh→0f(a+h)-f(a)h

Q: For which of the following does lim f(x) = 0? I. Inx f(x) = 99 f(x) = mx II. Înx III. f(x) = x99 %3D…

A: We have to find for which of the following limn→∞fx=0?Some…

Q: SX IF X <1 Let F(X) = (^(X-2) IF XZ1 a, Find Limx→1¹ and lim x⇒ F(x) b. does LIM X→1 f(x) exist? C,…

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Q: Evaluate: lim x→-1 x² + 2x + 1

A: Limit: Limit is a mathematical concept based on the concept of proximity that is used to give values…

Q: (A) Find the following Limits. x + 5 2. limy-3 f (x) if f(x) = }2x²+4 , x 4

A:

Q: If f(x)=√x find limx-4 f(x)-f(4) x-4

A:

Q: Find the following limits if they exist. Must show all work (analytically?): 1. X-2 lim (x) where…

A: Given that: 1. limx→-2f(x), where f(x)=-3x2+8, if x&lt;22x,          if x&gt;-2   NOTE: As per our…

Q: If 5-4x sf(x)s5-x for - 1<xs1, find lim f(x), lim f(x)%= f(x) =D

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Q: limits

A: L'Hospital's rule apply only when there is 0/0 for ∞/∞ form.

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: If f(w)=√4w-3, find lim h-0 f(w+h)-f(w) h [(w)].

A: